Primary hyperparathyroidism (PHPT) is a condition in which increased levels of parathyroid hormone (PTH) lead to high blood calcium. Most patients find out that they have PHPT after having routine blood tests, because often they feel no symptoms. However, high levels of PTH and calcium can lead to bone loss, kidney stones, muscle weakness, depression and stomach problems. The only available cure is surgery to remove the involved parathyroid gland(s). Currently, there is no specific medical treatment. In postmenopausal women with PHPT, estrogen therapy can reduce blood calcium levels, but only by a small amount. The purpose of this study is to evaluate the effectiveness of an experimental drug known as AMG 073 for the treatment of PHPT. It is hoped that this study will provide information on how well this medication controls the amount of PTH and calcium in the blood as well as provide additional safety information about AMG 073. This will be randomized, double-blind, placebo-controlled, multicenter, dose ranging clinical trial. Approximately 60 patients are expected to participate and will be randomized across 15 centers in the United States. The study is sponsored by Amgen Inc., who makes AMG073. Six different dose levels of AMG 073 will be investigated.